I know that many engines apply a penalty for a redundant rook, SF for example. But I wonder how many engines would apply the somewhat less obvious penalty for a redundant knight?

Pieces with same piece type, when repetitive, are of course due some penalty, as they do not coordinate quite well among themselves; in any case, different piece types coordinate better.

[d]6k1/1n6/3n2p1/7p/1P5P/6P1/8/R5K1 w - - 0 1
2 knights should be stronger than rook + pawn just by their values, but not here. Actually, white has excellent winning chances above.

Trying to fix this by changing the piece values, for example increasing rook value, might well backfire, as this would not be true for many other positions with different piece configurations. But giving a penalty just for a redundant knight would address the specific problem when one side has more than one knight.

[d]6k1/1b6/3n2p1/7p/1P5P/6P1/8/R5K1 w - - 0 1
If we change one of the knights for a bishop, already white has zero winning chances, so redundancy matters, as in the usual case the bishop value would not be quite different from the knight piece value.

[d]r1r3k1/4npp1/2n4p/p7/P4B2/2Q3P1/3N1P1P/6K1 w - - 0 1
It is impossible to draw this one with black. (see, black has 2 pairs of redundant pieces, first the rooks, and secondly the knights)

[d]r1r3k1/4bpp1/2n4p/p7/P4B2/2Q3P1/3N1P1P/6K1 w - - 0 1
But quite possible to draw this one with black, the only change being that black's knights are already not redundant.

So that, I really think that a redundant knight penalty is a must, especially in the endgame, where knights are also much slower and their redundancy is harshly felt. In the middlegame, I think knight redundancy is very small, as knights could find in this phase of the game good outpost squares, and even sometimes support each other in the fight for such squares, but still a slight measure of redundancy is felt.

I would give a redundant knight some 5-8cps normal values penalty in the middlegame, 10-15cps in the endgame. For SF, of course, values would be double.

What is your opinion of a redundant knight penalty?
Any author applying such a penalty?

I think your views on this are way too simplistic. As the Queens vs Knights end-games show, Knights cooperate much better with each other than mixed pieces do.

There is a well-known reason for penalizing a pair of Knights: it has no mating potential. How important this is depends on the total number of Pawns, though.

The first position you show is also favorable for white because of the Pawn spread. Pawns on both wings is an advantage against low-speed pieces like Knights per se, whether they come in pairs or not. Give white an f-Pawn in stead of a b-Pawn, and he doesn't stand any winning chances at all. Even shifting the Pawn to the c-file already seems to make the position quite hopeless for white's winning ambitions: the Knights can block the passer while protecting each other, and protect their own g-Pawn at the same time, leaving no weakness for the Rook to attack.

So this doesn't seem to have anything to do with redundancy. Just with Pawn structure evaluation and the absence of sliding pieces that can easily switch wing. Replace one of the Knights by a Modern Elephant, (which moves one square, or jumps two, both diagonally), and you will not be off much better, (if not much worse), despite the facts that the Knight and Elephant have completely different moves.

Lyudmil Tsvetkov wrote:I know that many engines apply a penalty for a redundant rook, SF for example. But I wonder how many engines would apply the somewhat less obvious penalty for a redundant knight?

You are wrong on both of your pre-supposition, so all the rest is not even worth reading:
1. stockfish does NOT have a redundant rook term. it was shown to be completely useless in testing and removed. In discocheck, I also arrived at the same conclusion.
2. knight redundancy is a seriously dubious concept. HGM has already explained this to you in lengthy details (elephantiasis effect), but as usual you did not listen, and you continue trying to teach your misconceptions anyway...

Theory and practice sometimes clash. And when that happens, theory loses. Every single time.

It might make sense to talk a bit about redundant pieces in general. I should have named this thread Redundant pieces, but never mind.

Of course, apart from knights, redundant rooks also deserve a penalty, and even bigger.

[d]r1r3k1/1p3pp1/p6p/8/5B2/1P1BN2P/P4PP1/6K1 w - - 0 1
Although in terms of piece values material is almost fully equal, white is much better here. And the distinction is not only in the 2 bishops, but also additionally in the fact that the 2 black rooks are redundant. This makes coordination among them much harder, or actually, the opposite side has a much better coordination. Redundancy is penalised precisely because of that: for lack of coordination among redundant pieces.

2 bishops, on the other hand, although of same piece type, are never redundant, as they control squares of different colour.

A redundant rook penalty should be bigger of course than a redundant knight penalty, first because redundant rooks are more vulnerable, and second because this type of redundancy is much more frequent, as on the opposite side you have th possibility for a large number of different minor piece configurations.

I think 1/3 bigger penalty than for knight should be OK, so some 15cps uniform penalty both for the middlegame and endgame is a good measure. For me, the penalty should be uniform as for once, rooks do not fight for outpost squares in the middlegame, and twice, the rook value usually gets higher in the endgame.

There are also other, subtler forms of redundancy.
A queen is redundant with a bishop, but only partially, as in its diagonal capacity the queen controls the same squares as the bishop, but not in its linear, file and rank movements capacity. (controlling squares of different colour does not count here, as the queen and bishops have completely different material values)

A queen is also redundant with a rook, but again only partially, as in their linear capacity both pieces control squares along files and ranks, same squares that is, but in its diagonal capacity the queen controls different squares from the rook.

These subtler forms of redundancy are of course felt, but less so. I would give both queen-bishop and queen-rook redundancies half the penalties of what a rook redundancy is due, so maybe some 7-8cps normal values, 15cps SF values, uniform for both middlegame and endgame.

[d]r3r1k1/1p3pp1/p3n2p/8/8/1PQ1B2P/P4PP1/6K1 w - - 0 1
The 2 black rooks are redundant, but the white queen is partially redundant with the white bishop too, they are both diagonal pieces.

[d]3rr1k1/1p3pp1/p1p1n2p/8/8/1PQ4P/P4PP1/4R1K1 w - - 0 1
The 2 black rooks are redundant, but the white queen is also partially redundant with the white rook, as they are both linear pieces.

[d]r3r1k1/1p3pp1/p1b1n2p/8/8/1PQ1B2P/P4PP1/4R1K1 w - - 0 1
The black rooks are redundant, but the white queen is redundant with both the white rook and the white bishop.

So that again, I would give redundant pieces the following redundancy penalties:

I think doing redundancy is very important, especially for people who care about material values. You simply can not tune material values well enough without also giving the corresponding redundancy penalty for the specific piece configuration.

How many authors do rook redundancy?
How many authors do subtler forms of redundancy, as queen and bishop and queen and rook redundancy?

Lyudmil Tsvetkov wrote:I know that many engines apply a penalty for a redundant rook, SF for example. But I wonder how many engines would apply the somewhat less obvious penalty for a redundant knight?

Pieces with same piece type, when repetitive, are of course due some penalty, as they do not coordinate quite well among themselves; in any case, different piece types coordinate better.

This makes little sense to me, especially for rooks. Two rooks can work very well in forming a "battery", that can control an open file, for example.

Perhaps I misunderstand "redundancy", especially if "many engines apply a penalty for a redundant rook".

hgm wrote:I think your views on this are way too simplistic. As the Queens vs Knights end-games show, Knights cooperate much better with each other than mixed pieces do.

There is a well-known reason for penalizing a pair of Knights: it has no mating potential. How important this is depends on the total number of Pawns, though.

The first position you show is also favorable for white because of the Pawn spread. Pawns on both wings is an advantage against low-speed pieces like Knights per se, whether they come in pairs or not. Give white an f-Pawn in stead of a b-Pawn, and he doesn't stand any winning chances at all. Even shifting the Pawn to the c-file already seems to make the position quite hopeless for white's winning ambitions: the Knights can block the passer while protecting each other, and protect their own g-Pawn at the same time, leaving no weakness for the Rook to attack.

So this doesn't seem to have anything to do with redundancy. Just with Pawn structure evaluation and the absence of sliding pieces that can easily switch wing. Replace one of the Knights by a Modern Elephant, (which moves one square, or jumps two, both diagonally), and you will not be off much better, (if not much worse), despite the facts that the Knight and Elephant have completely different moves.

I think we agreed that 3 queens do better vs 7 knights than against 3 knights and 4 bishops. There was sufficient game evidence for that. Jerry Donald also posted that 7 bishops perform better than 7 knights vs 3 queens.

It is also about pawn spread, but in 80-90% of cases pawns will be spread on both wings, so this is the natural state of things. Having pawns just on one wing is an exception. With pawn spread on both wings, 2 knights perform even worse than a single knight, so redundancy is felt.

Lyudmil Tsvetkov wrote:I know that many engines apply a penalty for a redundant rook, SF for example. But I wonder how many engines would apply the somewhat less obvious penalty for a redundant knight?

You are wrong on both of your pre-supposition, so all the rest is not even worth reading:
1. stockfish does NOT have a redundant rook term. it was shown to be completely useless in testing and removed. In discocheck, I also arrived at the same conclusion.
2. knight redundancy is a seriously dubious concept. HGM has already explained this to you in lengthy details (elephantiasis effect), but as usual you did not listen, and you continue trying to teach your misconceptions anyway...

So when was rook redundacy removed from SF?
The last time I checked SF code, a month ago, it was still there. I also know that at the end of last year someone submitted a test to remove redundant rooks, and it failed. This is on the framework history page.

Harm explained nothing, it is still not certain if 7 knights are better than 3 queens, however, the above debate has nothing to do with penalising 2 knights in a normal game, as 2 knights never defend each other the way a larger number of minor pieces, 7 knights for example, would. Those are simply differences of scale. I am talking about a normal game situation.

Lyudmil Tsvetkov wrote:I know that many engines apply a penalty for a redundant rook, SF for example. But I wonder how many engines would apply the somewhat less obvious penalty for a redundant knight?

Pieces with same piece type, when repetitive, are of course due some penalty, as they do not coordinate quite well among themselves; in any case, different piece types coordinate better.

This makes little sense to me, especially for rooks. Two rooks can work very well in forming a "battery", that can control an open file, for example.

Perhaps I misunderstand "redundancy", especially if "many engines apply a penalty for a redundant rook".

This is about assessment of different factors. 2 rooks deserving a bonus for an open file is quite apart from 2 rooks being redundant, as for example a pawn could be isolated and form part of the king shelter, or bishop be outposted and have very little mobility at the same time.

We are talking here of imbalance evaluation, and in most cases, like in the position of 3 minors vs 2 rooks, because of their bad coordination in comparison to the 3 minors, the rooks will quite probably never be able to form a doubled rook battery. So that redundancy only accentuates deficiencies.

[d]4r1k1/1pp2pp1/p1b1n2p/8/8/1PQ1N2P/P4PP1/6K1 w - - 0 1
2 piece configurations that lack any form of redundancy. A queen is never redundant with a knight.
Rook, bishop and knight are never redundant among themselves, as they control different squares.

[d]5bk1/1p1q1pp1/p5bp/8/2P5/1P2NBBP/P4PP1/2R3K1 w - - 0 1
2 bishops are never redundant with a knight or rook, but are redundant with a queen, so black deserves above a small penalty for partial queen-bishop redundancy. (you could penalise just one of the bishops, so partial redundancy could receive just a single penalty for a specific configuration, i.e. you do not need to penalise twice the queen in QRR, just one full rook redundancy and one partial queen-rook redundancy penalty)

The amount of scepticism how useful this actually is is really astounding, but redundancy really plays a very big role in chess. The fact that someone tried to apply redundancy and failed does not mean that it is inapplicable. You simply need the right approach.

But again, to the unbelievers, there were times in chess, prehistoric ones, but also more recent, when engines evaluated only material and passers, and did very bad. Until some years ago passers even did not get a special bonus for rank. Most thought this to be stupid, but it proved to be completely not like that. It is the same with different forms of redundancy: they are real, they are tangible and useful, and could be successfully implemented, after many failed attempts of course, but you need to open your eyes.

I really appreciate your many posts concerning evaluation. Although I haven't read each one---there are quite a few, after all ---I've thought about many of them.

Now please don't take this the wrong way, but the main effect of your posts has been to convince me that this is not the way to go. Too many terms, too much hidden overlap (non-orthogonality), too many artifacts of the human approach to chess, motivated by our very limited search abilities.

At a fundamental level, it seems to me that evaluation comes down to mobility and attack. Even the material value of pieces is simply more or less an encapsulation of their mobilities. Admittedly this is overly simplistic (and focused on the opening and midgame), but a position is good for us if we can move to lots of squares and if we attack a lot of enemy material. After all, the goal of the game is to reduce the opponent's mobility to zero while simultaneously attacking his most valuable piece!

You've almost inspired me to revisit my primitive engine and, after improving the basic move generation and search, to focus on an evaluation based on mobility + attacking. Mostly as an academic exercise, since any engine I create would be just for fun (and also pretty weak).